Low Latency Broadcast in Multi-Rate Wireless Mesh Networks

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Low Latency Broadcast in Multi-Rate Wireless Mesh
Networks

• LUO Hongbo

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Outline

• Introduction
• Heuristic Algorithms
• Discussion

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Introduction- Wireless Mesh Networks

• Mesh routers mesh clients
• Mesh routers have minimal mobility
• No strict constraint on power consumption

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Introduction- Low Latency Broadcast

• Energy-efficient broadcast
• Broadcast advantage is exploited
• Broadcast latency
• computed as the maximum delay between the
  transmission of a packet by a source node and its
  eventual reception by all the intended receivers.
• Multi-rate natures in WMNs

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Introduction- Transmission and
Interference Model

• Transmission model Pr Pt
• The transmission range is a decreasing function
  of transmission rate
• Interference Model
• The distance between the transmitter and receiver
  dij Ri
• No transmitter nk within a finite distance Rk
  (such that dkj ltRk) is transmitting
  concurrently.

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Introduction- Impact of Multi-rate Links

• (Interference range is 520m)

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Introduction- The Model Assumptions

• Single radio single channel
• Fixed transmission power and multi-rate broadcast
  by adjusting the modulation scheme
• Receiver based interference model

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Introduction- Optimization Problem

• Problem
• Minimize the broadcast latency with possibly
  multiple number of transmissions per node in a
  multi-rate
• wireless mesh network
• This problem is NP-Hard
• Key Issues
• Whether a node should broadcast and if so, to
  which of its neighbors
• The timing of these broadcasts.

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Heuristic Algorithm - Problem
Decomposition

• Topology Construction
• SPT
• CDS
• BIB
• WCDS
• Downstream Multicast Grouping
• Multiple transmission per node is allowed
• Transmission Scheduling

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Heuristic Algorithm - Broadcast Incremental
Bandwidth (BIB)

• Mathematical notations
• The mesh network can be represented as a graph
  G(V,E).
• denotes the direct unicast
  link between nodes i
• and j, which is associated with a transmission
  rate Rij.
• Basic Idea (from BIP)
• Initially, every node except the root node will
  be set to a cost with 1/Rij
• In each iteration, the node with the minimum of
  incremental cost will be added to the tree

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Heuristic Algorithm An Example with BIB
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Heuristic Algorithm An Example with BIB
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Heuristic Algorithm An Example with BIB
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Heuristic Algorithm Weighted Connected
Dominating Set (WCDS)

• MCDS performs poorly in multi-rate case
• Minimum WCDS problem
• For a given graph G (V,E), we suppose there
  are k different
• rates given by r1,r2,,rk, Let N(x,ri) denote
  the nodes that are
• reachable from node using rate ri.
  The aim is to find a
• subset Y y1,y2, in V and the broadcast
  rate wi for node yi
• such that
• Every element of V\Y is in
• The set Y is connected
• The weighted sum is minimal

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Heuristic Algorithm Weighted Connected
Dominating Set (WCDS)

• The basic idea of the algorithm
• We suppose the set C including the nodes which
  have received the message and are eligible to
  transmit.
• Initially, we make the source node s eligible to
  transmit, Cs
• In each iteration, for every eligible node c and
  rate r, we choose the (c, r) combination that
  maximizes the rate of increase of not-yet-covered
  nodes, as measured by f(c,r) N(c,r)\C r.

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Heuristic Algorithm An Example with WCDS
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f(c,r) 1
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Heuristic Algorithm An Example with BIB
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f(c,r) 21/2 1
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Heuristic Algorithm An Example with BIB
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f(c,r) 41/8 1/2
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Heuristic Algorithm An Example with WCDS
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Heuristic Algorithm Transmission
Scheduling

• Some Notations
• Vb Let Vbb1,b2,,bk V be the set of the
  branch points in the broadcast tree T
• b1 Source node
• Gb A directed graph(tree) Gb(Vb, Eb) such
  that (bi, bj) Eb if and only if it is an edge
  in the tree T
• t(bi) For every node bi Vb, we assign a cost
  t(bi) which is the minimum multicast transmission
  time it takes the node bi to transmit a
  fixed-size packet to all its children.
• Gc An undirected conflict graph Gc (Vc, Ec)
  such tat Vc Vb and (bi, bj) Ec if and only if
  the multicast of bi interferes with the reception
  of the children of bj in T.

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Heuristic Algorithm Transmission
Scheduling

• Problem Formulation
• Formally, a schedule can be defined as a mapping
  
• which gives the transmission time of node bi
  Vb. Given Gb,
• t(bi) and Gc, a valid schedule is one which meets
  the following
• constraints
• The source multicasts at time zero 0.
• 
  .
• For any edge , we have
• The objective is to find a valid schedule which
  minimizes the
• broadcast latency

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Heuristic Algorithm Transmission
Scheduling

• Basic idea of the greedy algorithm
• In each iteration, for each qualified node in Q
  q1,q2,,qm, we
• select the the node qi with the largest value of
  f(qi). The metric f(qi)
• is defined as follows
• Where e(qi) is the earliest possible multicast
  time for the node qi,
• and w(bi) is the time needed to reach all the
  descendants of bi in T
• in the absence of interference and can be
  written
• Where D(bi) denote the set of all descendants of
  bi in Gb. For any x
• in D(bi), let P(bi,x) denote the set of nodes on
  the path from bi to x.

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Heuristic Algorithm Transmission
Scheduling
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Discussion

• Lack of quantitative analysis
• Is the joint optimization via combing the routing
  and scheduling possible?
• Should mesh clients be considered?

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• Thanks!